AN INTRODUCTION TO PROGRESS MONITORING IN MATHEMATICS

P R E S E N T E R ’ S M A N U A L

AN INTRODUCTION TO PROGRESS

MONITORING IN MATHEMATICS

Anne FoegenPamela M. Stecker

AN INTRODUCTION TO

PROGRESS MONITORING IN MATHEMATICS

P R E S E N T E R ’ S M A N U A L

This publication was created for the Center on Instruction by Instructional Research Group. The Center is operated byRMC Research Corporation in partnership with the FloridaCenter for Reading Research at Florida State University;Instructional Research Group; the Texas Institute forMeasurement, Evaluation, and Statistics at the University of Houston; and The Meadows Center for PreventingEducational Risk at The University of Texas at Austin.

The contents of this document were developed undercooperative agreement S283B050034 with the U.S.Department of Education. The contents do not necessarilyrepresent the policy of the Department of Education, and youshould not assume endorsement by the Federal Government.

Editorial, production, and design support provided by RMC Research Corporation.

Preferred citation:Foegan, A., & Stecker, P. M. (2009). An introduction to progressmonitoring in mathematics: Presenter’s manual. Portsmouth,NH: RMC Research Corporation, Center on Instruction.

The Center on Instruction and the U. S. Department ofEducation retain sole copyright and ownership of this product.However, the product may be downloaded for free from theCenter’s website. It may also be reproduced and distributedwith two stipulations: (1) the "preferred citation," noted on thispage, must be included in all reproductions and (2) no profitmay be made in the reproduction and/or distribution of thematerial. Nominal charges to cover printing, photocopying, ormailing are allowed.

Copyright © 2009 by RMC Research Corporation

To download a copy of this document, visit www.centeroninstruction.org.

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CONTENTS

1 INTRODUCTION

1 Intended Audiences

1 Organization of the Session

2 Length of the Session

3 Research Foundations for Mathematics Progress Monitoring

5 Implementation Issues

7 A Caveat

8 SLIDES

85 READINGS IN MATHEMATICS PROGRESS MONITORING

92 ARTICLES ON THE EARLY HISTORY OF PROGRESS MONITORING

READING AND MORE RECENT APPLICATIONS

INTRODUCTION

This manual has been developed to support the presentation of An Introductionto Progress Monitoring in Mathematics, a professional development PowerPointcreated by the Center on Instruction. The presentation provides an overview ofmathematics progress monitoring and includes:

• a definition of progress monitoring,

• support in distinguishing progress monitoring from other forms ofassessment,

• basic concepts in the development and implementation of progressmonitoring tools, and

• examples of progress monitoring tools in mathematics at the elementaryand secondary grade levels.

Intended Audiences

This presentation has been designed to serve the wide array of individuals whohave an interest in the concepts, empirical basis, and concerns relevant to theimplementation of mathematics progress monitoring. Among those who mayfind value in this professional development experience are general educationtechnical assistance personnel; education policy makers at the local, state, and federal levels; and mathematics and mathematics education researchersand teacher educators. Please note that the presentation is not designed toprovide a complete, highly detailed training in the actual implementation ofprogress monitoring.

Organization of the Session

The full presentation contains three sections. The first section describesstudent progress monitoring and offers a general definition, as well as a samplegraph of a student’s progress monitoring data. The second section contrastsother assessment approaches that are often mistaken for progress monitoring.The third, and largest, section describes the features of progress monitoringand includes examples of existing measures available for elementary andsecondary students. This manual also includes references, a bibliography, andadditional potentially valuable resources.

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Length of the Session

A presentation of the full set of slides would result in a two hour session.Presenters can select slides to meet particular circumstances and audienceneeds. The following table provides suggestions for possible adaptedpresentations. We strongly encourage presenters to draw on their ownknowledge of mathematics progress monitoring and audience needs to designan effective presentation.

Possible Adapted Presentations

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1 hour

1 hour

1.5 hours

1–4, 43–77 (modifySlide 3 for Overview)IntroductionElementary MeasuresSecondary MeasuresResources

1–38, 76–77 (modifySlide 3 for Overview)IntroductionPM FoundationsResources

1–22, 26–60, 74–77(modify Slide 3 forOverview)IntroductionPM FoundationsMath PM DetailsElementary MeasuresResources

Share specific measures formathematics

Provide foundations inprogress monitoring withoutthe complexity of specificmeasures for specificage/grade levels

Provide background inprogress monitoring with anemphasis on elementarymeasures

Individuals familiar withgeneral progressmonitoring concepts

Individuals with nobackground in progressmonitoring whoseprimary interest is inunderstanding the general concept

Elementary levelprofessionals

Audience Purpose Slides and Content Length

(continued)

Research Foundations for Mathematics Progress Monitoring

This presentation is based on 30 years of research that dates to the Institute on Research in Learning Disabilities at the University of Minnesota. Originallydeveloped by Stan Deno and his colleagues, a form of progress monitoringcoined curriculum-based measurement (CBM) was created to give teacherstechnically adequate tools to monitor students’ progress and informinstructional decisions in a system of formative evaluation. The initial work inCBM focused on reading, which has historically received a greater proportion ofresearchers’ attention than has mathematics.

The research in progress monitoring has been characterized by Fuchs (2004)as occurring in three stages. Stage 1 research examines the technical adequacyof static, or one point in time, indicators of student performance in progressmonitoring. In this stage, much of the research involves examining the reliabilityand criterion validity of measures and determining the degree of correlationbetween the measures and other indicators of proficiency in mathematics. This research also examines the ability of static measures to predict futureoutcomes, such as passing a state standards tests. Stage 2 research involvesinvestigations of the slopes produced by repeated administrations of progressmonitoring measures over time. These studies explore the technicalcharacteristics of the slopes and the degree to which they reflect studentlearning in mathematics. Finally, Stage 3 research explores teachers’ use of the data to improve student achievement.

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1.5 hours

2 hours

1–14, 23–42, 61–77(modify Slide 3 forOverview)IntroductionPM FoundationsMath PM DetailsSecondary MeasuresResources

1–77 (full presentation)IntroductionPM FoundationsMath PM DetailsElementary MeasuresSecondary MeasuresResources

Provide background inprogress monitoring with anemphasis on secondarymeasures

Provide foundations inprogress monitoring andexamples of progressmonitoring measures inmathematics at both theelementary and secondarylevels

Secondary levelprofessionals

Individuals unfamiliar withprogress monitoring andinterested in options foravailable measures at alllevels

Audience Purpose Slides and Content Length

Possible Adapted Presentations (continued)

The majority of research studies on mathematics progress monitoringmeasures have been in Stage 1. Published work in this area has beenconducted for measures of early numeracy (i.e., Chard et al., 2005; Clarke &Shinn, 2004; VanDerHeyden, et al., 2004; VanDerHeyden, Witt, Naquin, & Noell,2001), elementary mathematics (i.e., Epstein, Polloway, & Patton, 1989; Fuchs,Fuchs, Hamlett, & Stecker, 1990; Fuchs, Hamlett, & Fuchs, 1998, 1999; Shinn& Marston, 1985), and middle school mathematics (Foegen, 2000; Foegen &Deno, 2001; Helwig, Anderson, & Tindal, 2002; Helwig & Tindal, 2002).

Stage 2 research has included two studies of growth on early numeracymeasures (Chard et al., 2005; Clarke & Shinn, 2004), several for elementarymeasures (i.e., Fuchs, Fuchs, Hamlett, Thompson, Roberts, Kubek, & Stecker,1994; Fuchs, Fuchs, Hamlett, Walz, & Germann, 1993), and two studies at themiddle school level (Foegen, 2000; Helwig & Tindal, 2002). Stage 3 researchhas been conducted for elementary mathematics measures developed byFuchs and her colleagues (i.e., Fuchs, Fuchs, & Hamlett, 1989; Fuchs, Fuchs,Hamlett, & Stecker, 1990, 1991). These studies have examined the effects ofproviding teachers with additional data based on skills analyses and expertsystem guidance (Fuchs, Fuchs, Hamlett, & Stecker, 1991), as well asstrategies to guide their use of progress monitoring, such as consultation orself-monitoring (Allinder & BeckBest, 1995; Allinder, Bolling, Oats, & Gagnon,2000). Stecker and Fuchs (2000) demonstrated that teachers who usedprogress monitoring data to design the timing and nature of instructionalmodifications effected significantly greater overall achievement for studentscompared to matched partners who received the same instruction and changesbut whose progress was not monitored. These studies have repeatedlydemonstrated that teachers can effect increased levels of student achievementwhen they use progress monitoring in mathematics.

The mathematics progress monitoring measures developed by Fuchs andher colleagues (Fuchs, Hamlett, & Fuchs, 1998, 1999) have been studied also ingeneral education settings with peer-assisted learning strategies (PALS). Thesestudies have relied on progress monitoring data to aid teachers in selectingskills for large-group and small-group instruction as well as for pairing studentsfor classwide peer tutoring (i.e., PALS). Although the PALS procedures may beconducted without benefit of progress monitoring data, research has supportedthe use of math PALS in conjunction with ongoing progress monitoringinformation to increase achievement among high-, average-, and low-performing

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students, including students with learning disabilities, in Grades 2–6 (e.g.,Fuchs, Fuchs, Bentz, Phillips, & Hamlett, 1994; Fuchs, Fuchs, Hamlett, Phillips,& Bentz, 1994; Fuchs, Fuchs, Phillips, Hamlett, & Karns, 1995). Although anexhaustive review of the research base for mathematics progress monitoringexceeds the scope of this presentation, a list of articles on the topic is providedat the end of this manual.

Implementation Issues

The distinctions between the methods used to develop progress monitoringmeasures hold important consequences for education professionals who are deciding which measures to select. Presenters of this professionaldevelopment session should be well-versed in the advantages anddisadvantages of each approach in order to best respond to audience questions.

Approaches to the development of progress monitoring measures.

One aspect of progress monitoring covered in this presentation is the methodused to develop the measures. Fuchs (2004) made a distinction betweencurriculum sampling and robust indicators as two alternative approaches to thedevelopment of progress monitoring measures. Curriculum sampling involvescreating measures by sampling the instructional curriculum such that eachprobe represents a proportional sampling of the annual curriculum. Thisapproach is best represented by the measures developed by Fuchs, Hamlett,and Fuchs (1998, 1999). An advantage of this approach is that students’ probedata can be analyzed by skill type to identify particular areas of strength andweakness at both the classroom and individual student levels. These data allowteachers to make more informed decisions about how to modify the content oftheir instruction. Other advantages include the direct link to the instructionalcurriculum and the ability to evaluate how well students maintain and generalizepreviously taught skills and concepts. The limitations of curriculum samplinginclude the need to create measures for each grade level, the possibility thatthe measures are specific to a particular curriculum and may not work as well with other curricula, and the fact that the administration durations forcurriculum-sampled measures are often substantially longer than those forrobust indicators.

The second approach, robust indicators, uses an empirical process toidentify tasks or problem types that are correlated with proficiency in the

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content domain. In elementary mathematics, research on robust indicators has focused almost exclusively on proficiency in basic facts. It is important to emphasize that a robust indicator is just that: an indicator. Clearly, basic facts are not the “whole” of the mathematics curriculum at any grade level.However, to the extent that proficiency with basic facts is correlated withoverall proficiency in mathematics, this task can serve as a robust indicator.

The development process for robust indicators involves conducting researchto determine whether the proposed measure is correlated with other indicatorsof proficiency in mathematics. The advantages of the robust indicator approachinclude the potential to use the measures to monitor student growth acrossmultiple grade levels, the independence from any particular curriculum materials or instructional approach, and the efficiency of administration forthese measures. The limitations of this approach include the inability to deriveinstructional recommendations regarding specific skills, the lack of directconnection to the instructional content, and the inability to use the measures to evaluate the maintenance and generalization of previously taught content.

Responding to progress monitoring data. Although this presentationfocuses on the core concepts of progress monitoring and the options availableamong measures for progress monitoring in mathematics, it does not addresshow teachers should respond to progress monitoring data. This topic is beyondthe scope of this presentation, but presenters must be aware that instructionaldecision making lies at the very heart of progress monitoring. Teachers whobegin to use a progress monitoring system will produce data showing thatsome students are not making acceptable progress. Teachers must havesupport (in the form of consultation or professional development) that preparesthem to respond in this situation. Some types of progress monitoring data (e.g., those developed using curriculum sampling) may illustrate which skills or concepts might be most beneficial for additional instruction. Other types of progress monitoring measures indicate problems but offer less direction for solving them. Administrators, professional development experts, andconsultants need to be prepared to provide teachers with scientifically basedmethods or promising practices that have the greatest likelihood of improvingthe achievement of low-performing students.

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A Caveat

Session presenters must have a thorough understanding of the conceptsunderlying mathematics progress monitoring and the tools (measures) used to implement it. The talking points and reference citations in this manual cannot substitute for a rich background knowledge and/or extensive experience in implementing progress monitoring. This manual is not sufficient for use in isolation. Presenters with limited expertise should read widely aboutmathematics progress monitoring and engage with practitioners and otherprofessionals using mathematics progress monitoring to learn about thelogistical issues and challenges that practitioners face.

Therefore, this presentation should be used for informational, rather thantraining, purposes. It describes the foundations of progress monitoring and the options available for measures at the elementary and secondary levels.More thorough training would be needed to prepare individuals to implement a system of progress monitoring. Such training can be found through the U.S. Department of Education’s National Center for Student ProgressMonitoring (http://www.studentprogress.org). This website includes the training materials (PowerPoint presentations, manuals, and handouts) thataccompanied progress monitoring workshops and institutes conducted in 2005, 2006, and 2007. This information is updated periodically. Web articles on progress monitoring and presentation materials for national conferences also can be located on this website.

Note: Portions of this presentation have been adapted from slides takenfrom mathematics training materials (from the Summer Institutes) located onthe National Center for Student Progress Monitoring website:http://www.studentprogress.org.

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SLIDE 1

Background InformationPresenters should be well versed in progress monitoringsystems. The purpose of presentation may vary depending ontargeted audience. (Refer to table of possible adaptedpresentations on pages 2–3 in this manual.)

Talking PointsThis presentation focuses on progress monitoring principles and practices in the area of mathematics.

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SLIDE 2

Background InformationThis slide indicates the source of this presentation—theCenter on Instruction—and lists the Center’s partnerorganizations. You may want to display this slide during “down times” in your presentation to provide some context for the participants.

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SLIDE 3

Talking PointsThe purpose of this presentation is to provide participants withan overview of mathematics progress monitoring that includesthe following elements:• a definition and description of progress monitoring,

• support in distinguishing progress monitoring from other forms of assessment,

• basic concepts in the development and implementation of progress monitoring tools,

• examples of progress monitoring tools in mathematics at the elementary and secondary gradelevels, and

• a brief list of resources that provide additional information about progress monitoring.

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SLIDE 4

Background InformationThis slide must be included in ALL presentation variations ofthis material.Talking PointsThe use of specific measures as illustrations throughout thispresentation is intended as a means of increasing participants’comprehension of the material being presented and not as an endorsement of any specific products.

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SLIDE 5

Talking PointsProgress monitoring data are used to assess student learningacross time. That is, formative evaluation allows teachers tojudge student learning in an ongoing fashion. This informationis used to help teachers formulate decisions about theadequacy of student progress and the necessity of makinginstructional modifications.

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SLIDE 6

Talking PointsTeachers use test results for a variety of decision-makingpurposes. Formative evaluation informs teachers’ decisionmaking in an ongoing manner. One well-known type offormative evaluation is progress monitoring.

Progress monitoring involves ongoing data collection todetermine the adequacy of student progress toward a specified long-term goal. Although any ofthe progress monitoring scores may be compared to the level of the goal, progress monitoringprocedures also involve examination of the rate of student improvement. Drawing a line of best fitthrough the student’s data provides a trend line that can be compared to the expected rate ofimprovement that would be required for achieving the goal at the specified time.

Using progress monitoring data requires that teachers make decisions on a periodic basisabout whether student progress is sufficient to ultimately meet academic goals or whetherprogress appears insufficient to meet the goal. If the student is not progressing well, the teacherwould decide to modify the instructional program.

Progress monitoring can be used on a frequent basis to judge the overall effectiveness ofinstruction for particular students. Teachers use progress monitoring information to modifyinstructional practices, regroup students for instruction, change motivational strategies, and soforth, and then they evaluate the result of those instructional changes on student performance. Inthis manner, teachers formatively develop instructional programs to better meet particular studentneeds.

Supplemental InformationExamples for drawing trend lines and setting goals can be found in Summer Institute materials atthe National Center on Student Progress Monitoring: http://www.studentprogress.org.

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SLIDE 7

Talking PointsFor measures and procedures to qualify as progressmonitoring, several features must be addressed. They must betechnically adequate, showing strong reliability and validity.Students should not have the opportunity to memorize theactual items used on the tests, so equivalent alternate formsof the measures must be used over time. The short measures must be sensitive enough to capturestudent change (i.e., either growth or deterioration). Procedures are standardized, so thatmeasures are given in the same way each time and for the same length of time. Standard rulesare applied for scoring, so student responses are evaluated the same way regardless of theperson who performs the scoring. Progress monitoring involves the administration of relativelybrief measures that can be given frequently. By definition of the Technical Review Panel for theNational Center on Student Progress Monitoring, progress monitoring measures should be givenat least monthly with decisions made about the adequacy of student progress in order to qualifyas “true” progress monitoring measures. For students who are at academic risk, measurement canoccur as often as once or twice weekly. Measures are designed to be relatively brief, so they canbe given often without sacrificing much instructional time for assessment.

Supplemental ReferencesSeminal article and historical perspective of development of curriculum-based measurement (aresearch-validated form of progress monitoring):

Deno, S. L. (1985). Curriculum-based measurement: The emerging alternative. ExceptionalChildren, 52, 219–232.

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SLIDE 8

Background InformationThis measure illustrates only one example of progressmonitoring in mathematics. Other examples of mathematicstools are provided later in the presentation.

Talking PointsThis measure illustrates one way to assess student progress inmathematics problem solving. This is the first page of a three-page measure that could beadministered to students in Grade 4. The items on this measure represent the types of conceptsand application skills that would be taught across the year. Students take alternate forms of thesesame types of items on a frequent basis. As teachers address more of the content and asstudents make progress in mathematics, student scores should increase across the year. Otherexamples of mathematics progress monitoring measures are provided later in the presentation.

Supplemental InformationThis example of progress monitoring illustrates the curriculum-sampling approach in contrast tothe robust-indicator approach. These two types of approaches used in the development ofprogress monitoring tools are described later in the presentation.

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SLIDE 9

Background InformationThis graph was generated through the Excel spreadsheetprogram.

Talking PointsThis graph shows progress monitoring data for one student.Round dots indicate the number of correct student responseson each progress monitoring assessment. Here, scores for correct responses are provided for twoinstructional interventions across about 17 weeks. Three baseline scores were collected duringthe first week. The diamond indicates the median score for baseline performance. In this example,the end-of-year goal was set at 30 (the triangle). The diagonal line connecting median baselineperformance (i.e., the diamond) with the end-of-year goal (i.e., the triangle) is the goal line. Thegoal line illustrates the anticipated rate of growth this student needs to demonstrate throughoutthe year in order to meet the year-end goal.

After collecting baseline performance, the teacher devised an instructional program for thisstudent. Initial implementation is indicated by the first vertical line on the graph. The teacheradministered and graphed the scores from the progress monitoring measures once a week. Duringthis first intervention phase, the student did not perform at the desired rate. The teacherdetermined that he would fall short of the year-end goal if instruction remained static. Theteacher made another instructional modification (shown by the second vertical line).

The teacher continued to monitor student progress weekly to assess the effectiveness of thesecond intervention. The student appeared to be improving dramatically. Teachers typically usestandard decision-making rules to interpret graphed data, allowing them to formatively developmore effective instructional interventions for each student.

Supplemental InformationAlthough beyond the scope of this presentation, goal-setting strategies typically involve the use ofnormative information about student performance levels and growth rates. More specificinformation about goal setting can be obtained from mathematics presentation materials (SummerInstitutes) on the National Center for Student Progress Monitoring website:http://www.studentprogress.org.

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SLIDE 10

Talking PointsProgress monitoring is often confused with other types ofevaluation procedures. Consequently, this next sectiondiscusses the differences between progress monitoring andother common forms of assessments. First, we begin bydescribing assessment practices that teachers use frequentlybut that are not considered to be progress monitoring.

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SLIDE 11

Talking PointsThree types of assessments that are not progress monitoringare screening tools, diagnostic assessments, and curriculum-embedded assessments. Screening tools are typically broad-based and are used to target students who could bepotentially at risk for developing difficulties in that domain.Scores typically are compared to pre-established benchmarks, often a particular percentile or cutscore. If the student does not score at or above this criterion, it is unlikely that he or she willdevelop typically in that academic area without some type of intervention. Most screeninginstruments are given only once or several times during the year (e.g., fall, winter, spring).Although some screening tools also may be used for progress monitoring when alternate formsare provided, by definition, assessments must be used on at least a monthly basis for decisionmaking to be considered progress monitoring measures.

Diagnostic assessments provide more in-depth information about a student’s performance inparticular conceptual or skill areas. For example, a diagnostic assessment may help a teacher todetermine that a student has difficulty with subtraction with regrouping when 0s are used in theminuend.

Curriculum-embedded tests examine student performance on the content that has been taught.Examples of curriculum-embedded tests include teacher-made tests and tests that are publishedas a part of curricular series. Although screening, diagnostic, and curriculum-embeddedassessments may yield useful information, none of these types of measures are considered to beprogress monitoring tools.

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SLIDE 12

Talking PointsTeachers probably use curriculum-embedded assessmentsmost frequently as a part of their instructional program.Curriculum-embedded tests help determine whether studentshave learned the critical skills in the curriculum. The curricularprogram may include its own version of chapter/unit/booktests, or teachers may make their own tests. Teachers use curriculum-embedded tests to trackwhether students have mastered particular skills and knowledge. Typically, the set of items on thetest represents a limited number of problems, concepts, or skills, and decisions are made aboutstudent mastery of short-term objectives. These assessments often look much like the materialsused during instruction.

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SLIDE 13

Talking PointsWhen teachers develop their own curriculum-embedded tests,they typically follow a particular sequence of steps. If theydecide to check student performance during instruction, theyfirst determine the skill and/or concept to be instructed andassessed. They develop multiple assessment forms that reflectthose particular skills or concepts. Then the teacher administers an alternate form of theassessment on a frequent basis to check whether the student is learning the skill. Whenperformance indicates that the skill has been mastered, the teacher moves on to a new skill forinstruction and devises a new set of tests to assess mastery of this new skill. This type of teach-and-test routine is probably used most frequently with low-achieving students to determine whenmastery occurs and when a new skill(s) can be taught.

Note: an example of another type of curriculum-embedded assessment (publisher developed) isdescribed on the next slide.

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SLIDE 14

Talking PointsTeachers frequently use curriculum-embedded tests (i.e.,chapter or unit tests) that are provided by the publisher of thebasal or textbook series utilized in the classroom. Teacherstypically use these types of tests with the entire class toevaluate whether students have learned the content covering aparticular portion of the curriculum.

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SLIDE 15

Background InformationSlides 15–22 illustrate how teacher-developed, curriculum-embedded assessments play out in an individualized tutoringcontext. A fictitious fourth-grade teacher is tutoring a low-achieving student on computational skills.

Talking PointsThis example illustrates a curriculum-embedded approach to assessment within a tutoringcontext. Mr. Jones is tutoring a student who is experiencing difficulties with fourth-gradecomputational skills. Mr. Jones first determines on which skills within an instructional sequencehis student is weak. He creates alternate forms of criterion-referenced tests that contain multipleproblems of this type. He then sets a benchmark, or criterion, for mastery of the skill or concept.Additional instruction is provided, and alternate forms of these criterion-referenced assessmentsare given frequently to determine student mastery of the skill. When his student reaches thecriterion for mastery, Mr. Jones moves to a new skill for instruction and develops a new set ofcriterion-referenced tests to match the new skill being instructed.

This is NOT an example of progress monitoring, however, because it is specific to one skill or concept.

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SLIDE 16

Talking PointsMr. Jones delivers instruction on a skill and gives an alternateform of the criterion-referenced test every day or a couple oftimes per week to check mastery. When the student reachesthe criterion for mastery, he moves to a new skill forinstruction.

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SLIDE 17

Talking PointsThis example provides a hypothetical sequence ofmathematics computational skills in a fourth-grade curriculum.Mr. Jones determines that his student has difficulty withmulti-digit addition with regrouping, so he focuses instructionon this skill.

Supplemental InformationA number of slides, including this one, have been adapted from the mathematics training(Summer Institutes) provided by the National Center on Student Progress Monitoring:http://www.studentprogress.org. Individuals may go to the website to learn more specificinformation about progress monitoring procedures.

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SLIDE 18

Talking PointsHere is an example of a criterion-referenced test that Mr. Jones developed to check whether his student wasmastering multi-digit addition with regrouping. He gives analternate form frequently (e.g., daily or a couple of times perweek) to evaluate student mastery of the skill. He sets at least8 of 10 problems correct on three successive occasions as the criterion for mastery of this skill.All of these problems assess addition with regrouping even if the particular difficulty level of theitems varies somewhat, depending on the number of regroupings required or their placementwithin the problems.


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SLIDE 19

Talking PointsMr. Jones teaches multi-digit addition with regrouping andassesses his students’ performance a couple of times eachweek until they student reach the set criterion. Here a studenthas met the criterion for mastery (i.e., at least 8 of 10problems correct on three, successive occasions), so theteacher changes the focus of instruction to the next skill.


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SLIDE 20

Talking PointsThe teacher targets the next skill in the sequence forinstruction. In this curriculum, Mr. Jones plans instruction formulti-digit subtraction with regrouping next.

Supplemental InformationA number of slides, including this one, have been adaptedfrom the mathematics training (Summer Institutes) provided by the National Center on StudentProgress Monitoring: http://www.studentprogress.org. Individuals may go to the website to learnmore specific information about progress monitoring procedures.

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SLIDE 21

Talking PointsFirst, Mr. Jones develops a new set of alternate measures toassess student performance on multi-digit subtraction withregrouping. Again, he sets the criterion for mastery as at least8 problems correct out of 10 on three successive occasionsand gives his student an alternate form of this test on a twice-weekly basis.


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SLIDE 22

Talking PointsMr. Jones has organized his tutoring sessions to insure thatthe student is progressing through the skills of the fourth-grade curriculum. Once the student has achieved mastery ofmulti-digit addition, Mr. Jones begins instruction in multi-digitsubtraction with regrouping. He gives a “curriculum-embeddedmeasure” twice weekly until his student reaches the criterion for mastery. By examining thisgraph, we see that, although the student has now supposedly learned two skills, themeasurement task has changed from one skill to another. Mr. Jones doesn’t really know with thisevaluation system whether the student has maintained mastery of the first skill (multidigitaddition with regrouping).

Now that Mr. Jones’s student has reached the criterion for mastery on multidigit subtractionwith regrouping, he moves to instruction in basic multiplication facts. However, Mr. Jones mustdevise a new set of curriculum-embedded tests to assess proficiency on this skill. One of thecritical features of curriculum-embedded assessment is that a close link exists between theinstructional content and the content that is assessed. As the instructional content changes, sodoes the assessment content.

Although Mr. Jones is using teacher-developed, curriculum-embedded tests to determinesuccessive mastery of specific skills (problem types), he is not really able to judge whether thestudent is on-track toward accomplishing the year-end goal. Curriculum-embedded assessmentsfor different skills vary in their level of difficulty, so performance cannot be compared from oneskill to the next. Consequently, Mr. Jones is not able describe his student’s overall progressthrough the curriculum toward the year-end goal. He is able to gauge student performance onlywithin each specific skill area.


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SLIDE 23

Background InformationSlides 23–25 illustrate how curriculum-embedded assessmentsplay out in typical general education classrooms. The slidesuse a fictional ninth-grade algebra teacher and her annualcurriculum for the illustration.

Talking PointsLet’s consider how curriculum-embedded assessment might look at the secondary level. ConsiderMs. Harwood’s situation. This example is typical of many secondary mathematics classrooms inthe country.

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SLIDE 24

Background InformationThe list of topics on this slide was drawn from the chaptertitles of a commonly used Algebra 1 textbook.

Talking PointsThis list reflects the chapters in Ms. Harwood’s textbook. Mostpublishing companies provide teachers with assessments,such as chapter and unit tests or performance assessment activities, to use with the instructionalmaterials. If Ms. Harwood is teaching Chapter 3 on solving linear equations, it is likely that shewould use the test or assessment materials provided by the publisher to evaluate her students’learning on Chapter 3. This is an example of curriculum-embedded assessment.

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SLIDE 25

Background InformationThe list of topics on this slide was drawn from the chaptertitles of a commonly used Algebra 1 textbook.

Talking PointsAfter completing Chapter 3, Ms. Harwood would next move toChapter 4 on graphing linear equations and functions. If shewere using a curriculum-embedded approach to assessment, she would again turn to thepublishers’ assessment materials or perhaps to assessments she has designed herself in order toevaluate her students’ learning of the content in Chapter 4. One of the critical features ofcurriculum-embedded assessment is that there is a close link between the instructional contentand the content that is assessed. As the instructional content changes, so does the assessmentcontent.

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SLIDE 26

Background InformationThe purpose of Slides 26 and 27 is to help audience membersrecognize the limitations of curriculum-embeddedassessments. These limitations also will provide a context forconsidering the features of progress monitoring assessments,many of which provide a direct remedy to these limitations.

Talking PointsAlthough curriculum-embedded tests may yield some information about specific skills/concepts,these assessments are associated with several limitations. First, when the teacher changes thecontent of the assessment to a new skill (e.g., from addition with regrouping to subtraction withregrouping), maintenance of previously learned skills is not monitored. Also, generalization oflearned information to other skills cannot be evaluated when the focus or content of theassessment changes to a new skill and is limited to only one type of problem or operation.

A second limitation is related to technical aspects of the tests and testing procedures.Reliability and validity are critical features of assessments that are used for decision-makingpurposes. However, most curriculum-embedded tests made by teachers or developed by textbookpublishers have unknown reliability and validity. Another limitation relates to the misguidedassumption that the greater number of skills that are assessed and judged as adequate, the betterthe student will do on year-end achievement tests. Of particular concern is the problem thatstudents may progress through the sequence of chapter- or skill-based tests with adequatescores, but still not be synthesizing or generalizing this information at a level that translates intocompetence in mathematics as reflected on high-stakes tests.


Supplemental References


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SLIDE 27

Talking PointsSeveral other limitations occur with curriculum-embeddedassessments. Although the sequence of skills for instructionmay appear logical (i.e., one skill seems easier than the nextskill taught later) or teachers may be following a district-levelpacing guide, the order of skills for instruction and assessmentis not based on research. In other words, a different skill sequence could support better learningfor particular students. Additionally, when the content changes on the new assessments, so doesthe difficulty level of the tests. Thus, the student’s progress for one type of skill cannot becompared directly to progress made on another type of skill. Moreover, these curriculum-embedded assessments typically provide information only on limited skill sets. As a result,curriculum-embedded assessments often do not illustrate how a student actually progressesthrough the curriculum. Instead, these curriculum-embedded assessments show only performanceon specific skills or concepts.




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SLIDE 28

Background InformationThis section, Slides 28–40, provides the definition and furtherdescription of critical features of progress monitoring systems.

Talking PointsThis section covers what makes progress monitoringdistinctive. Although some features are shared with othertypes of assessments, progress monitoring measures are developed and used in very specific ways.

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SLIDE 29

Talking PointsIn progress monitoring, teachers collect data in an ongoingfashion to determine the progress students are making andwhether that progress is sufficient to ultimately meet year-endgoals. By judging the adequacy of student progress, teachersalso are indicating whether their instructional methods areworking appropriately (i.e., bringing about the desired effect) for particular students.

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SLIDE 30

Talking PointsTeachers use progress monitoring data to determine astudent’s rate of improvement in response to particularinstructional methods. If the rate of improvement (trend line)does not match (is less steep than) the expected rate ofprogress (goal line), the teacher should make instructionalchanges to better meet student needs.

Actual student responses (e.g., error analysis) on the progress monitoring measures mayindicate where the student is having difficulty, allowing the teacher to target particular skills orconcepts for remediation. By using progress monitoring data in this way—that is, testing out theeffects of programmatic changes on student progress—teachers can build, formatively, moreeffective instructional programs over time for particular students.

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SLIDE 31

Talking PointsResearch confirms that progress monitoring data producemeaningful information about overall student performance in an academic area and can show students’ rate ofimprovement in the curriculum over time. These scores alsoare sensitive to student change in terms of either improvementor deterioration.


Supplemental ReferencesMany of the experimental-contrast design studies addressing the use of progress monitoring datafor enhancing student learning and improving teachers’ instructional decision have beenconducted by Lynn and Doug Fuchs and their colleagues at Peabody College of VanderbiltUniversity. Several key references addressing this question in mathematics are included here:

Fuchs, L. S., Fuchs, D., & Hamlett, C. L. (1989). Effects of alternative goal structures withincurriculum-based measurement. Exceptional Children, 55, 429–438.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Stecker, P. M. (1990). The role of skills analysis incurriculum-based measurement in math. School Psychology Review, 19 (1), 6–22.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Stecker, P. M. (1991). Effects of curriculum-basedmeasurement and consultation on teacher planning and student achievement in mathematicsoperations. American Educational Research Journal, 28, 617–641.

Stecker, P. M., & Fuchs, L. S. (2000). Effecting superior achievement using curriculum-basedmeasurement: The importance of individual progress monitoring. Learning DisabilitiesResearch and Practice, 15 (3), 128–134.

Stecker, P. M., Fuchs, L. S., & Fuchs, D. (2005). Using curriculum-based measurement to improvestudent achievement: Review of research. Psychology in the Schools, 42, 795–819.

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SLIDE 32

Talking PointsStudies demonstrate that student scores on progressmonitoring measures correlate well with student performanceon other types of academic measures, such as standardized,norm-referenced tests and states’ high-stakes measures.Progress monitoring systems have been emphasized in recentyears because research shows greater overall achievement gains among students whose teachers use such systems compared to teachers who use their own evaluation and instructionalplanning methods.


Supplemental ReferencesMany of the experimental-contrast design studies in this field have been conducted by Lynn andDoug Fuchs and their colleagues at Peabody College of Vanderbilt University. Several keyreferences addressing this question in mathematics are included here:





Stecker, P. M., Fuchs, L. S., & Fuchs, D. (2005). Using curriculum-based measurement to improvestudent achievement: Review of research. Psychology in the Schools, 42, 795–819.

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SLIDE 33

Background InformationThis slide and the next one illustrate the overall set ofprocedures for conducting progress monitoring.

Talking PointsTeachers use progress monitoring as a systematic way to makeinstructional decisions based on student data.

First, the teacher evaluates the student’s current performance on the progress monitoringmeasures. This baseline information may be used to target an ambitious but realistic goal for theend of the year. The teacher provides instruction and continues to monitor student progress on afrequent basis.

At periodic intervals, the teacher evaluates whether student progress appears adequate tomeet the established goal by the end of the year. The teacher poses this question: “If thestudent’s progress continues in this same manner for the rest of the year, is it likely that he or shewill achieve the year-end goal?” If student progress appears insufficient, the teacher responds bymaking one or more instructional modifications. If the student is actually doing better thananticipated (i.e., trend of student data is steeper than the goal line), the teacher would raise thelevel of the goal. Teachers should not leave low expectations in place when the student appearsto be making progress faster than expected

Supplemental InformationThe teacher should never adjust the goal downward. Research indicates that students tend towork harder and achieve more when teachers set ambitious goals, whether or not studentsactually meet those particular goals.

When the student’s rate of progress mirrors the rate established by the goal line, the teachermay keep the same instructional program in place and continue to collect progress monitoringdata, allowing him or her to continue evaluating the adequacy of student progress and makeinstructional modifications or raise goals as needed.

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SLIDE 34

Background InformationThis graph depicts the progress monitoring process across theyear for one student.

Talking PointsThis graph illustrates the use of progress monitoring todevelop an effective instructional program. Here, the teacherhas administered the same type of progress monitoring tool to Donald throughout the year todetermine his rate of improvement. In October, the teacher used baseline performance (anaverage of six scores collected during the month) to set an end-of-year goal. The red line connectsaverage baseline performance with the year-end goal and shows the rate of progress Donaldneeds to make throughout the year to attain his goal. Donald’s teacher continues to assess hisperformance with similar measures to monitor Donald’s responsive to her instruction. She thencompares Donald’s actual rate of progress to the red goal line to see if he is moving alongadequately toward the long-term goal.

Look at Donald’s progress during November and December. He seemed to have changed littleduring November and December. Consequently, his teacher modified instruction in January to tryto better meet Donald’s needs. This instructional intervention is shown on the graph by the solidvertical line at the end of December.

Although Donald’s performance level increased during January (reasoned to be a result of theinstructional modification), the slope of his improvement in January did not match his goal line(i.e., the anticipated slope of improvement required to meet the end-of-year goal). Donald’steacher adjusted instruction again in February in an effort to boost Donald’s achievement.

Donald’s performance improved somewhat in February, but it started to stabilize (or evendeteriorate) in early March. The teacher made yet another instructional adjustment in March.How would you describe Donald’s progress during March? Do you think he is likely to meet hisend-of-year goal?

Supplemental InformationThe dotted vertical line on the graph shows the end of data collection for baseline. Donald’saverage performance during baseline is marked on the dotted vertical line. Donald’s teacher usedthis average (often a mean or median score) as the beginning point for drawing the goal line.Teachers use baseline information as one piece of information for establishing an appropriatelyambitious goal. Information about goal setting can be found in the materials provided by theNational Center on Student Progress Monitoring (see below).

A number of slides, including this one, have been adapted from the mathematics training(Summer Institutes) provided by the National Center on Student Progress Monitoring:http://www.studentprogress.org. Individuals may go to the website to learn more specificinformation about progress monitoring procedures.

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SLIDE 35

Talking PointsProgress monitoring measures must be administered oftenenough to provide sufficient data for judging student progress.The testing schedule is determined by student need. Progressmonitoring is especially critical for low-achieving students;teachers may opt to administer measures more frequently tothese students (once or twice weekly). If students seem to be doing well, a teacher might checktheir progress only monthly. To meet the definition of true progress monitoring, however, datamust be collected at least once a month.

If teachers are collecting data once or twice a week, they will have sufficient data every monthor two to draw conclusions about the overall effectiveness of their instructional program and stillhave enough time to implement instructional modifications as needed.

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SLIDE 36

Talking PointsAlthough teachers might be most concerned about their low-achieving students, they may monitor the progress of allstudents. Typically, low-achieving students are monitored untilthey reach levels of proficiency. Teachers evaluate studentperformance patterns using data-based decision rules. Theserules indicate when goals should be raised or when instruction should be modified.

Supplemental InformationSpecific data-based rules can be found in the mathematics training materials (Summer Institutes)on the National Center for Student Progress Monitoring website: http://www.studentprogress.org.

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SLIDE 37

Talking PointsProgress monitoring measures are developed in very specificways. For example, alternate forms of the measures arecreated so that students do not memorize problems from testto test. However, the difficulty level of the measures shouldnot change throughout the year. Each measure represents theproficient or desired performance expected by the end of the year. With progress monitoringmeasures, students are taking shortened versions of the year-end test. By keeping the difficultylevel constant, teachers can compare student scores on the graph to reveal improvement ordeterioration in achievement.

The amount of time allocated to take the test should also remain constant. Otherwise, scorescannot be compared. The time allotment should not allow students to finish the test. This permitsteachers to capture growth for comparatively high-achieving students. Task completion is not agoal of progress monitoring. The focus should stay on capturing student change and growth.

Supplemental InformationTask difficulty could vary throughout the year as long as the measures are equated and anchoredto a common scale or metric.

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SLIDE 38

Talking PointsBecause progress monitoring graphs involve comparisons of a student’s scores over time, test conditions need to remainconstant, including the difficulty of the tests and the timeallotted for taking them. Tests are relatively short, so teachers can give them frequently without sacrificing a lot ofinstructional time. Teachers determine scores using standardized procedures and specified scoring rules.

Raw scores, or counts, are the primary data for graphing rather than percent correct. Teachers should not use progress monitoring data for student grades (e.g., as percentage of items completed correctly). Rather, progress monitoring helps teachers evaluate overall studentresponse to the instructional program, as indicated by the adequacy of student progress.

Supplemental InformationThe time allocated for test-taking should remain constant for tests given within a grade level.However, the amount of time may differ by grade level, depending on the types of skills andconcepts being assessed. In mathematics, measures typically range from 2–15 minutes, with most measures taking 2–8 minutes.

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SLIDE 39

Background InformationThe information in this slide is drawn from Fuchs’ (2004)article, “The Past, Present, and Future of Curriculum-BasedMeasurement Research” (see reference below). This article isan excellent resource on basic approaches to the developmentof CBM measures and stages of research to establish thosemeasures as viable for progress monitoring. Presenters are strongly encouraged to read thisarticle carefully.

Talking PointsIn a 2004 article in School Psychology Review, Lynn Fuchs described two approaches to creatingprogress monitoring measures. These approaches are particularly relevant to mathematics.

The first approach, curriculum sampling, systematically draws items from the annual curriculumin proportions that reflect their comparative instructional emphasis. For example, curriculum-sampled progress monitoring measures in the early elementary grades would have more problemsinvolving addition and subtraction of whole numbers. Those in the later elementary grades wouldhave whole number problems and problems with fractions, decimals, and percents. Each progressmonitoring measure samples from the entire year’s instructional curriculum. At the beginning ofthe school year, students may not be able to answer a large portion of the problems, but, asinstruction progresses, they are expected to become more proficient.

Progress monitoring measures using robust indicators consist of more global behaviors thateither require students to integrate the range of skills taught in the annual curriculum or arehighly correlated with other indicators of proficiency in the annual curriculum.



Fuchs, L. S. (2004). The past, present, and future of curriculum-based measurement research.School Psychology Review, 33, 188–192.

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SLIDE 40

Talking PointsAs mentioned, a curriculum-sampled mathematics progressmonitoring measure draws from the entire annual instructionalcurriculum. Teachers need to alert students that there may bequestions on the measure that they haven’t learned yet.

These data are still useful, though, for conducting skillsanalyses and determining strengths and weaknesses for individuals and groups of students.Teachers will need to continually keep in mind which concepts have not yet been taught. Also,each measure provides data on the degree to which students are maintaining and generalizingskills and concepts taught earlier in the academic year.

Curriculum sampling has some disadvantages. First, because these measures represent theannual curriculum, they are often longer and take away more time from instruction. Second,because each measure draws from a specific curriculum, it may not generalize to other curricularprograms. Research has not yet clearly answered the question of generalizability amongcurriculum-sampled measures. Finally, because instruction changes with each grade level,different measures must be created specifically for each grade level’s curricular emphases, callingfor a greater commitment to and investment in measure development.

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SLIDE 41

Talking PointsRobust indicators are also referred to as general outcomemeasures in the literature. As mentioned earlier, theseassessments (or probes) do not span the full range of problemtypes included in a curriculum. The concept of indicators isparticularly important with this approach. These measures donot represent the whole instructional curriculum but they serve as indirect indicators ofproficiency in this whole.

A classic example of a robust indicator in reading is oral reading fluency. This simple measure(the number of words read correctly from a passage of text in one minute) clearly does not reflectthe entire range of skills and concepts included in any reading curriculum. However, students’performance on this measure highly correlates with overall proficiency in reading, including,decoding, fluency, and comprehension. An example from mathematics is estimation, a robustindicator used at the middle school grades.

The process for developing robust indicators differs from creating measures using curriculumsampling, where measures are developed through a careful analysis of the skills and conceptsfrom the entire annual curriculum. In the development of robust indicators, an empirical processdetermines which potential tasks produce sufficiently strong correlations with other indicators ofmathematics proficiency.

Supplemental InformationFoegen (2000) and Foegen & Deno (2001) have published research on the use of estimation as aprogress monitoring measure for middle school that represents the robust indicator approach.Other examples of robust indicators in mathematics would include basic facts in single or mixedoperations.


Foegen, A. (2000). Technical adequacy of general outcome measures for middle schoolmathematics. Diagnostique, 25(3), 175–203.

Foegen, A., & Deno, S. L. (2001). Identifying growth indicators for low-achieving students inmiddle school mathematics. Journal of Special Education, 35, 4–16.

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SLIDE 42

Talking PointsThe advantages of robust indicators tend to mirror thedisadvantages of curriculum sampled progress monitoringmeasures. Because robust indicators are not tied to a specificcurriculum program nor to a particular grade level, they can beused across both curricular programs and grade levels. Inaddition, they also tend to take less time to administer because there is less variability in theproblem types.

Similarly, the advantages of curriculum sampling measures become the disadvantages ofrobust indicators. Robust indicators may not have a clear link to the instructional content. Inaddition, because these measures do not sample the range of instructional skills and concepts,they are less useful to teachers in providing skills analysis information that can directly guideinstructional changes. And, robust indicators have less value in assessing students’ maintenanceand generalization of the skills they have learned throughout the year.

Along with considering the advantages and disadvantages of the two types of approaches,schools should consider what measures are available for the grade in which they want toprogress monitor, the reliability and validity evidence for the measures, and other importantpractical issues such as cost and ease of use.

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SLIDE 43

Background InformationMost of the work in progress monitoring in mathematics hasbeen done at the elementary level. A couple of progressmonitoring systems have extended computation and problemsolving into the middle school levels. The following slidesprovide examples of progress monitoring programs usedprimarily in the elementary grades.

Talking PointsSeveral commonly used programs for monitoring mathematics progress in the elementary yearsare highlighted next.

Many of the examples provided in the coming sections have been taken from commerciallyavailable products. Those products do not necessarily represent the policy of the U.S. Departmentof Education, and you should not assume endorsement by the Federal Government or the Centeron Instruction.

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SLIDE 44

Talking PointsCurriculum-based measures in mathematics have been usedsuccessfully to monitor the progress of students in theelementary grades since the 1980s. Both types of measures,curriculum sampling and robust indicators, have provensuccessful at this level. Today, several commercially preparedWeb-based systems incorporate progress monitoring in mathematics.

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SLIDE 45

Talking PointsWith curriculum sampling, items that represent the criticalskills for the year-long curriculum and/or grade-level standardsare included on the actual progress measures. Alternate formstest the same types of skills, although the actual numerals inthe problems change. Allocated time for test taking staysconstant across the year for a particular grade level, but time may vary for different grade levels.

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SLIDE 46

Talking PointsSome forms of progress monitoring systems contain items forcomputation only or for concepts and applications only. Someforms combine computation and problem solving. Whichevermethod is used, the types of problems remain constant acrossthe year. Because these same skills are tested repeatedly,teachers can analyze student performance with respect to particular problem types. The teachercan develop a skills profile to help him in instructional planning.

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SLIDE 47

Background InformationSlides 47–55 illustrate several progress monitoring programsthat use curriculum sampling.

Talking PointsSeveral examples of progress monitoring systems using thecurriculum sampling method for test development arehighlighted next.

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SLIDE 48

Background InformationSome practitioners may have been taught to score the numberof correct digits in all the intermediate steps of solving aproblem instead of just the number of correct digits in theanswer. Data for normative growth and benchmark informationfound in mathematics materials (Summer Institutes) of theNational Center on Student Progress Monitoring (http://www.studentprogress.org) are based onscoring correct digits in answers.

Talking PointsA book of blackline masters of 30 alternate probes for each grade level 1–6 is available. Thesemeasures were developed by sampling computational skills deemed necessary for grade-levelpromotion in the Tennessee statewide curriculum in the late 1980s–1990s.

Depending on the specific grade level, allotted time for test administration is 2–6 minutes, andspecific scoring rules are applied for evaluating student answers. The number of correct digits inanswers is the datum used for graphing progress.

Supplemental InformationBlackline masters of 30 alternate probes for each grade level 1–6 are available fromhttp://www.proedinc.com. These measures have been used in a variety of classroom-basedresearch projects. This work has demonstrated the measures’ technical adequacy, typical studentgrowth rates, and usefulness for teachers’ instructional planning and subsequent contribution toenhanced student achievement.


Fuchs, L. S., Hamlett, C. L. & Fuchs, D. (1998). Monitoring basic skills progress: Basic mathcomputation (2nd ed.). Austin, TX: PRO-ED. Available: http://proedinc.com.

Quite a few studies have incorporated these measures in their research procedures. The followingexperimental-contrast studies examined the use of progress monitoring on student achievement.Additional studies can be found in the reference list at the end of this manual.


Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Stecker, P. M. (1990). The role of skills analysis incurriculum-based measurement in math. School Psychology Review, 19(1), 6–22.


Stecker, P. M., & Fuchs, L. S. (2000). Effecting superior achievement using curriculum-basedmeasurement: The importance of individual progress monitoring. Learning DisabilitiesResearch and Practice, 15(3), 128–134.

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SLIDE 49

Background InformationThese probes were developed as part of the first computerizedmathematics progress monitoring system when Apple IIcomputers were popular in schools. The computer program isno longer available. However, 30 alternate probes for eachgrade level (1–6) are provided in one book of blackline mastersfor computation, which is available for purchase through PRO-ED. A more current hybrid of thistype of system (i.e., containing some similar features but also a number of clearly distinctivefeatures) is the Web-based system Yearly Progress ProTM by CTB/McGraw-Hill.

Talking PointsThis test is one of 30 alternate forms for fourth-grade computation provided by the MonitoringBasic Skills Progress system. Depending on grade level, test administration time varies from 2–6minutes. Recommended allotted time for this probe is 3 minutes. Problems are placed randomlyon the page, but the same problem types are tested on each form. Each alternate form contains25 problems. Problems are scored in terms of the number of correct digits in answers.

Supplemental InformationNumerals are randomly generated within problems to the extent that the particular skill allows.For example, if the skill were addition with no regrouping for two, 2 x 2 digit numbers and thefirst number was 64, then the ones place in the second number could vary only from 0–5 and thetens place could vary only from 1–3.

This and other slides in this presentation were adapted from the mathematics training(Summer Institutes) provided by the National Center on Student Progress Monitoring:http://www.studentprogress.org. Individuals may go to the website to learn more specificinformation about progress monitoring procedures.


Fuchs, L. S., Hamlett, C. L. & Fuchs, D. (1998). Monitoring basic skills progress: Basic mathcomputation (2nd ed.). Austin, TX: PRO-ED. Available: http://proedinc.com.

Quite a few studies have incorporated these measures in their research procedures. The followingexperimental-contrast studies examined the use of progress monitoring on student achievement.Additional studies can be found in the reference list at the end of this manual.





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SLIDE 50

Background InformationData for normative growth and benchmark information found in mathematics materials (Summer Institutes) of the National Center on Student Progress Monitoring(http://www.studentprogress.org) are based on the number of correct blanks completed.

Talking PointsA book of blackline masters of 30 alternate probes for each grade level 2–6 is available forpurchase. These progress monitoring measures were developed by sampling concepts andapplications skills deemed necessary for grade-level promotion in the Tennessee statewidecurriculum in the late 1980s–1990s.

Depending on the specific grade level, allotted time for test administration is 6–8 minutes.Specific scoring rules are applied when evaluating student answers. Some problems requireseveral parts, so each answer blank completed within the problem is scored as right or wrong.The number of correct blanks completed is the datum used for graphing student progress.

(Note: an example of this measure appears on the next slide.)

Supplemental InformationBlackline masters of 30 alternate probes for each grade level 2–6 are available for concepts andapplications from http://www.proedinc.com.


Fuchs, L. S., Hamlett, C. L. & Fuchs, D. (1999). Monitoring basic skills progress: Basic mathconcepts and applications. Austin, TX: PRO-ED. Available: http://proedinc.com.

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SLIDE 51

Background InformationThese probes were developed as part of the first computerizedmathematics progress monitoring system when Apple IIcomputers were popular in schools. The program is no longeravailable for purchase. However, 30 alternate probes for eachgrade level (2–6) are provided in one book of blackline mastersfor concepts and applications, which is available for purchase through PRO-ED. Although theconcepts and applications blackline masters can be purchased separately from the computationblackline masters, both sets of probes were developed using the same principles andmethodology. A more current hybrid of this type of system (i.e., containing some similar featuresbut also a number of clearly distinctive features) is the Web-based system Yearly Progress ProTMby CTB/McGraw-Hill.

Talking PointsThis slide shows the first page of a three-page test at the fourth-grade level in concepts andapplications. With Monitoring Basic Skills Progress, computation probes are given separately fromconcepts and applications. Six minutes are allocated for work on this three-page concepts andapplications test.

Depending on grade level, test-taking times vary from 6–8 minutes. The concepts andapplications problems on each probe require computational skills for figuring many of theanswers, but the level of computational skill required for problem completion is no more difficultthan the problem types included on the fourth-grade level computation probes. Concepts andapplications probes are scored in terms of number of correct blanks (or response opportunities)completed correctly. For example, problem 1 contains three answer blanks, so a student couldearn up to three points on Problem 1. However, only one point could be earned on Problem 2,because it contains only one answer blank. The same types of concepts and applicationsproblems are tested on alternate forms, and the number of problems remains the same on eachgrade level.



Fuchs, L. S., Hamlett, C. L. & Fuchs, D. (1999). Monitoring basic skills progress: Basic mathconcepts and applications. Austin, TX: PRO-ED. Available: http://proedinc.com.

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SLIDE 52

Talking PointsYearly Progress ProTM is a Web-based version of progressmonitoring in mathematics. Tests are taken at the computer for15 minutes, although students may have paper and a pencil forfiguring answers. Students select the correct choice for mostof the items, although some problems require typing thenumerals for the answers. Both computational and problem-solving items are included in the 30 problems at each grade level 1–8.

(Note: these features continue on the next slide.)

Supplemental InformationAn audio option allows students to hear the problems being read aloud. This option may beimportant for students who have weak reading skills.

Supplemental ReferencesInformation about this Web-based program can be found at http://www.mhdigitallearning.com.

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Background InformationAlthough developed using similar methods to Monitoring BasicSkills Progress, data for normative growth and benchmarkinformation found in the mathematics materials (SummerInstitutes) of the National Center on Student ProgressMonitoring (www.studentprogress.org) may not apply to YearlyProgress ProTM measures. Yearly Progress ProTM measures require entire problems to be scoredas correct or incorrect, regardless of the number of digits correct in answers or the number ofsteps in the problem.

Talking PointsProblems are scored as correct or incorrect with graphed scores reflecting the percentage of 30items answered correctly. Skills analyses are available at both the class and student level. Inaddition, instructional exercises are provided by the system for each of the problem types tested.Therefore, teachers may assign particular instructional exercises to students who appear to needadditional practice.

Supplemental InformationSchool or district administrators also may have access to the program and can look at studentprogress by class or grade.

Supplemental ReferencesInformation about this Web-based program can be found at www.mhdigitallearning.com.

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SLIDE 54

Talking PointsInstructional exercises are provided for each skill. Teachersmay assign exercises that include screens with demonstration,guided practice (including corrective feedback), andindependent practice (5-problem quiz). This slide shows onescreen of an instructional exercise for a geometry skill, but italso illustrates the format for item presentation on the progress monitoring probes. Each problemis presented one at a time on the progress monitoring measures. Students may move forward orbackward through the probe.


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SLIDE 55

Talking PointsThis screen illustrates the type of information in YearlyProgress ProTM. A different screen shows all the clusterstested at this grade level, but this screen illustrates theanalysis for the eight skills in the sixth-grade algebra cluster.Level of mastery (red = not mastered; yellow = partiallymastered; green = mastered) is shown for each skill for every student in this class.

Supplemental InformationEach alternate form tests the same set of clusters (e.g., algebra) each time, although the specificskills within each cluster may vary somewhat from test form to test form. Items are presentedsimilarly to what might be seen on standardized, norm-referenced assessments or high-stakestests. Mastery information for skills analysis is based on the last three items on recent tests foreach of the skills in the cluster.


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SLIDE 56

Background InformationSlides 56–60 illustrate two progress monitoring programs thatuse robust indicators.

Talking PointsRobust indicators are skills that correlate well with overallproficiency in the subject area. Several monitoring systemsinclude a type of robust indicator as the method for assessing student progress.

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SLIDE 57

Talking PointsEdcheckup is a Web-based system that uses the robustindicator approach. Cloze Math provides a basic facts probe, inwhich a mixed set of 80 problems of addition, subtraction,multiplication, and division facts are presented on two pages.Empty boxes appear in any position within the problem. Forexample, in an addition problem, a student may need to give the answer for the sum or for anaddend. Students have 2 minutes to fill in the boxes.

Students may take a paper-pencil test, for which teachers score the measures and enterstudent scores into the program. The electronic scoring feature may be selected instead, in whichstudents see the probe and type in answers at the computer. When 2 minutes have elapsed, theprogram scores the answers, provides the score for the student, and saves the score in thesystem for the teacher. Cloze Math is designed to be used for students in Grades 2–6. Graphs of student progress are provided as well as other types of feedback for the teacher or school administrator.

(Note: an example of this measure appears on the next slide.)

Supplemental ReferencesInformation about this Web-based program can be found at www.edcheckup.com.

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SLIDE 58

Talking PointsThis slide shows the top portion of an electronic math clozeprobe in progress. The student already has typed in some ofthe answers. The test will disappear after 2 minutes and thenwill save and display the student’s score.

Supplemental InformationThe math cloze probes are designed for use with students in Grades 2–6. Edcheckup future plansinclude the incorporation of a Quantity Math measure for students in kindergarten through secondgrade. With this measure, students select the larger of two numbers presented.

Supplemental ReferencesInformation about this Web-based program can be found at http://www.edcheckup.com.

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Talking PointsAIMSweb is another Web-based progress monitoring system.Measures are downloaded and printed for students to take aspaper-pencil tests. A variety of mathematics measures isprovided, but all options include computational skills only.AIMSweb provides probes that have been developed boththrough the robust indicator approach and through the curriculum sampling approach.

With the robust indicator approach, 2-minute basic facts probes may be selected for singleoperations or for a mixture of operations (i.e., mixed facts of addition and subtraction, mixed factsof multiplication and division, or mixed facts across all four operations). With the curriculumsampling approach, mixed skills including computation beyond basic facts are included as 2-minute probes for Grades 1–3 and as 4-minute probes for Grades 4–8. Like the other Web-based systems discussed here, graphs of student progress are provided as well as other types of feedback for the teacher and/or school administrator.

(Note: examples of this measure appear on the next slide.)

Supplemental ReferencesInformation about this Web-based program can be found at www.aimsweb.com.

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SLIDE 60

Talking PointsThese AIMSweb measures illustrate the use of robustindicators and curriculum sampling. Presented here areexamples of mixed basic facts for addition and subtraction on the left and eighth grade mixed computation measure onthe right.

Supplemental ReferencesInformation about this Web-based program can be found at www.aimsweb.com.

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SLIDE 61

Background InformationAlthough some tools exist for mathematics progressmonitoring in the secondary grades, the research evidence and the range of tools is limited to a small body of literatureconducted by Helwig and his colleagues and Foegen and hercolleagues. Yearly Progress Pro has mathematics measuresavailable for students through Grade 8; research is currently underway to establish the technicalcharacteristics of these measures.

Research work is also underway by Foegen and her colleagues to develop progress monitoringtools in algebra. These measures are included in this presentation to illustrate the types of toolsthat might be valuable for secondary mathematics teachers. Examples of the measures andtechnical reports with the research conducted to date on the measures are available on theProject AAIMS website (www.ci.hs.iastate.edu/aaims).

This next section of slides (Slides 61–73) provides examples of current work to developmathematics progress monitoring measures for secondary mathematics, specifically in algebra.

Talking PointsIn this section of the presentation, we take a closer look at some examples of measuresdeveloped to measure secondary students’ progress in mathematics.


Foegen, A. (2000). Technical adequacy of general outcome measures for middle schoolmathematics. Diagnostique, 25 (3), 175–203.

Foegen, A., & Deno, S. L. (2001). Identifying growth indicators for low-achieving students inmiddle school mathematics. Journal of Special Education, 35, 4–16.

Helwig, R., Anderson, L., & Tindal, G. (2002). Using a concept-grounded, curriculum-basedmeasure in mathematics to predict statewide test scores for middle school students with LD.Journal of Special Education, 36, 102–112.

Helwig, R., & Tindal, G. (2002). Using general outcome measures in mathematics to measureadequate yearly progress as mandated by Title I. Assessment for Effective Intervention, 28 (1),9–18.

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SLIDE 62

Background InformationThis section of the slides highlights the work of Project AAIMS(Algebra Assessment and Instruction: Meeting Standards), afederally funded research project directed by Anne Foegen atIowa State University. Project AAIMS was funded for a three-year period from January 2004 through December 2006. TheProject AAIMS website (www.ci.hs.iastate.edu/aaims) includes descriptions of activities, samplesof the algebra probes, copies of technical reports, and links to peer-reviewed studies.

Talking PointsAlthough many options exist for mathematics progress monitoring tools at the elementary level,very little research and development work has been completed for the secondary grades. Themiddle school measures developed to date focus on general mathematics and are oftenextensions of existing elementary measures.

This section highlights the work of Project AAIMS (Algebra Assessment and Instruction:Meeting Standards), a grant project funded by the U.S. Department of Education, Office of SpecialEducation Programs. This project developed and validated progress monitoring measures for usein pre-algebra and first year algebra. Four of the potential measures investigated in ProjectAAIMS are described next. These measures include some that have been developed usingcurriculum sampling and others that represent the robust indicators approach to development.

More information about Project AAIMS can be found on the project’s websitewww.ci.hs.iastate.edu/aaims.


Foegen, A. (2008). Algebra progress monitoring and interventions for students with learningdisabilities. Learning Disability Quarterly, 31, 65–78.

Foegen, A., Olson, J. R., & Impecoven-Lind, L. (in press). Developing progress monitoring measuresfor secondary mathematics: An illustration in algebra. Assessment for Effective Intervention33 (4).

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SLIDE 63

Talking PointsThese four types of algebra progress monitoring measures areshown next. For each measure, we first will look at a sampleof the measure and then discuss development, administration,and scoring procedures.

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SLIDE 64

Talking PointsThis slide shows the first of two similar pages of the BasicSkills probe that has been developed by Project AAIMS.

Supplemental InformationA full copy of a Basic Skills probe can be downloaded from theResources page of the Project AAIMS website,www.ci.hs.iastate.edu/aaims.

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Talking PointsThe Basic Skills probes were developed using the robustindicators approach. These probes are appropriate for use inpre-algebra or first year algebra courses. Each probe consistsof 60 items that represent five different types of skills (seesecond bullet). The problems were selected to represent basicskills in algebra that students with a basic level of proficiency in first-year algebra should be ableto perform with reasonable fluency.

The problems also include skills that, according to teacher observations, represent barriers tostudents becoming proficient in algebra, including applications of the distributive property andcomputations involving integers. Students work on the Basic Skills probes for 5 minutes. Scoresare determined by counting the number of problems completed correctly.

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Talking PointsThis slide shows the first of two pages of an AlgebraFoundations probe.

Supplemental InformationA full copy of an Algebra Foundations probe can bedownloaded from the Resources page of the Project AAIMSwebsite, www.ci.hs.iastate.edu/aaims.

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Talking PointsThe Algebra Foundations probes also were developed usingthe robust indicators approach. Like the previous measure,they are appropriate for use in pre-algebra and first-yearalgebra courses. The Algebra Foundations probes weredeveloped to reflect core concepts and skills that are essentialto understanding algebra. This probe’s concepts and skills align more closely with the content of a pre-algebra course than a first-year algebra course. Five core concepts and skills were used to create the problems included in the probe (see third bullet). Students work on this probe for 5 minutes. Their scores are determined by counting the number of correct responses; 50 possiblecorrect responses are included in each probe.

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Talking PointsThis is the first of three pages of a Translations probe. On thesubsequent pages, the format of the information presented inthe top row (the A, B, C, D options) varies. On the secondpage, the first row consists of data tables; on the third, thefirst row contains graphs.

Students complete this probe by determining “matches” between different representations ofthe same relationship between two variables. For example, Equation A (y = x) is represented ingraphic form in the third graph in the second row, so the student would write an “A” in the blanknext to that graph. Similarly, the first data table (in the third row) shows that each of the listedvalues of x is associated with a y value of 1.5. This data table would match to Equation C, y = 1.5.

Supplemental InformationA full copy of a Translations probe can be downloaded from the Resources page of the ProjectAAIMS website, www.ci.hs.iastate.edu/aaims.

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Background InformationThis task was adapted from a problem type incorporated in theConnected Mathematics Project (CMP) curriculum, a NationalScience Foundation-funded middle school curriculumdeveloped at Michigan State University. More informationabout this curriculum is available on the CMP website, whichcan be found below.

Talking PointsThe Translations measure is also a robust indicator, but it represents a very different type of task.The Translations probe has very little emphasis on symbol manipulation and more emphasis onconceptual understanding of the relationships between two variables and the different modeswith which these relationships can be represented or modeled. Project AAIMS staff created thisprobe by adapting a type of problem in the Connected Mathematics Project (CMP) curriculum formiddle school students that involved matching different representations of the same relationshipbetween two variables.

In this task, students translate among four different representations: equations, data tables,graphs, and story scenarios. There are 43 problems on this probe; students have 7 minutes towork. Because this probe involves a multiple-choice format, the scoring scheme takes intoaccount the possibility that student responses are based on guessing. A student’s final score iscomputed by subtracting the number of incorrect responses from the total number of problemscorrect. Students are instructed that they should not make wild guesses when responding to thisprobe and that a penalty is applied to their score for guessing.

Supplemental ReferencesThe Connected Mathematics Project website is located at http://connectedmath.msu.edu.

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Talking PointsThis final example of an algebra progress monitoring measureis a Content Analysis-Multiple Choice probe. The slide showsthe first of two pages of this measure. The problems werecreated by sampling key ideas from the first two-thirds of atraditional Algebra 1 textbook. As with the other examples ofprogress monitoring measures, the problems are placed in random order. This strategy contrasts with typical curriculum-embedded assessments, which usually place problems on an assessment in order of their difficulty or in the same order in which they were presented in the instructional curriculum.

Supplemental InformationA full copy of a Content Analysis-Multiple Choice probe can be downloaded from the Resourcespage of the Project AAIMS website, www.ci.hs.iastate.edu/aaims.

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Talking PointsOf the algebra progress monitoring measures highlighted sofar, this is the only one that was developed using curriculumsampling. All three of the districts participating in ProjectAAIMS were using the same textbook series (a traditionalAlgebra 1 text), so this probe was designed to provide a closermatch to the teachers’ instructional materials.

The probe consists of 16 problems. Students have 7 minutes to complete as many problems as possible. The problems were drawn from the first two-thirds of the textbook and are presented in a multiple-choice format. Students are instructed to show their work in order to earn partial credit.

Each problem is worth up to 3 points. Students earn full credit by circling the correct answerfrom among the four choices or by writing the correct answer as part of their written work. Ascoring rubric is used to assign 2, 1, or 0 points to problems for which students have made anattempt at the solution, but were not able to correctly solve the problem. If a student circles anincorrect answer and does not show any written work, the response is considered a guess andthe student loses 1 point as a penalty for guessing.

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SLIDE 72

Background InformationThe next two slides provide a brief summary of the researchresults on the algebra progress monitoring measures at thetime when this presentation was developed. The most currentinformation about the measures will be available from theProject AAIMS website.

Talking PointsProject AAIMS staff have conducted a series of research studies on the algebra progressmonitoring measures. The results obtained to date have demonstrated that three of the measures(Basic Skills, Algebra Foundations, and Content Analysis-Multiple Choice) have adequate levels ofreliability, criterion validity, and sensitivity to growth.

Supplemental InformationComplete information about the research conducted on the algebra progress monitoring measurescan be obtained through the Technical Reports link on the Research page of the Project AAIMSwebsite, www.ci.hs.iastate.edu/aaims. As published studies become available, they will be listedunder the Publications link on the Research page.

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Background InformationThis slide and the previous one provide a brief summary of theresearch results on the algebra progress monitoring measuresat the time of development of this presentation. The mostcurrent information about the measures will be available fromthe Project AAIMS website.

Talking PointsLess research has been conducted on the Translations measure because it did not align well withthe traditional instructional materials being used in the districts participating in Project AAIMS.Research is continuing to refine the algebra measures and to examine the degree to whichteachers’ use of the data can improve student achievement.

Supplemental InformationMore complete information about the research conducted on the algebra progress monitoringmeasures can be obtained through the Technical Reports link on the Research page of the ProjectAAIMS website, www.ci.hs.iastate.edu/aaims. As published studies become available, they willbe listed under the Publications link on the Research page.

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SLIDE 74

Background InformationThis slide illustrates summary information on a range ofprogress monitoring tools across content areas. Practitionersshould consider the extent of research support available for aparticular set of progress monitoring tools as they makeselection decisions.

Talking PointsThis slide shows a portion of a screen from the National Center on Student Progress Monitoringunder the “Tools” section, highlighting results from annual reviews of progress monitoringproducts that have been submitted to the Center’s Technical Review Committee. Vendorsvoluntarily submit their product information for review.

This chart shows the standards and ratings obtained for each of the progress monitoringsystems submitted for review. Adequate technical features as well as adherence to acceptablestandards of progress monitoring procedures are important considerations when selectingprogress monitoring tools.

Supplemental InformationThe standards that are evaluated for each measure include: reliability, validity, sufficiency ofalternate forms, sensitivity to student improvement, provision of adequate yearly progress (AYP)benchmarks, improvement of student learning or teacher planning, and specification of rates of improvement.

Supplemental ReferencesThis tools chart can be found at the National Center on Student Progress Monitoring website,www.studentprogress.org under “Tools” at www.studentprogress.org/chart/chart.asp.

The National Center on Response to Intervention’s website also contains information onstudent progress monitoring. www.rti4success.org.

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Background InformationThis source was cited on slide 39. It identifies curriculumsampling and robust indicators as two approaches to thedevelopment of progress monitoring measures. It alsodescribed three stages of research necessary to establishprogress monitoring measures.

Stage 1 research examines the technical adequacy of the measures as static indicators ofstudent performance at one point in time. Stage 2 research examines the technical characteristicsof slopes derived from repeated measurement of student performance as indicators of studentrogress. Stage 3 research examines teachers’ use of progress monitoring data to effect improvedstudent achievement.

Talking PointsThis article by Lynn Fuchs includes a description of the two approaches to developing progressmonitoring measures: curriculum sampling and robust indicators. It also describes three stages ofresearch necessary to establish the viability of progress monitoring measures.

Supplemental ReferencesAlthough the article by Fuchs (2004) was cited specifically within this PowerPoint presentation, a long list of articles related to progress monitoring, most of which include mathematics, isavailable at the end of the Presenter’s Manual that accompanies this PowerPoint presentation.

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Talking PointsMore information about the measures briefly described in thispresentation can be found at these websites.

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Talking PointsPresenters who are interested in training materials formathematics progress monitoring at the elementary level maywish to consult the resources for training available through theU.S. Department of Education’s National Center for StudentProgress Monitoring: www.studentprogress.org. This websiteincludes all training materials (i.e., PowerPoint presentations, manuals, and handouts) thataccompanied recent Summer Institutes of half-day or day-long workshops. Workshops on progressmonitoring in mathematics can be downloaded for Summer Institutes conducted in 2005, 2006,and 2007. Web articles on progress monitoring as well as presentation materials for nationalconferences also can be located here.

The U.S. Department of Education’s Research Institute for Progress Monitoring(www.progressmonitoring.org) contains a great deal of information about progress monitoringresearch, including a searchable database of research articles related to curriculum-basedmeasurement. Investigators affiliated with this national center continue to conduct research inprogress monitoring, especially in areas that have been largely underrepresented, includingexamination of measures for older students and for students with cognitive disabilities.

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READINGS IN MATHEMATICS PROGRESS MONITORING

Allinder, R.M. (1996). When some is not better than none: Effects of differentiatedimplementation of curriculum-based measurement. Exceptional Children, 62,525–535.

Allinder, R. M., & BeckBest. (1995). Differential effects of two approaches tosupporting teachers’ use of curriculum-based measurement. School PsychologyReview, 24, 285–296.

Allinder, R. M., Bolling, R. M., Oats, R. G., & Gagnon, W. A. (2000). Effects ofteacher self-monitoring implementation of curriculum-based measurement andmathematics computation achievement of students with disabilities. Remedial& Special Education, 21(4), 219–226.

Allinder, R. M., & Oats, R. G. (1997). Effects of acceptability on teachers’implementation of curriculum-based measurement and student achievement inmathematics computation. Remedial and Special Education, 18(2), 113–120.

Allinder, R.M., & Swain, K.D. (1997). An exploration of the use of curriculum-basedmeasurement by elementary special educators. Diagnostique, 23, 87–104.

Bentz, J. L., & Fuchs, L. S. (1993). Teacher judgment of student mastery of mathskills. Diagnostique, 18(3), 219–232.

Burns, M. K., VanDerHeyden, A. M., & Jiban, C. L. (2006). Assessing theinstructional level for mathematics: A comparison of methods. SchoolPsychology Review, 35, 401–418.

Bryant, B. R., & Rivera, D. P. (1997). Educational assessment of mathematics skillsand abilities. Journal of Learning Disabilities, 30(1), 57–68.

Cohen, M., & Leonard, S. (2001). Formative assessments: Test to teach. PrincipalLeadership, 1, 32–35.

Calhoon, M. B., & Fuchs, L. S. (2003). The effects of peer-assisted learningstrategies and curriculum-based measurement on the mathematicsperformance of secondary students with disabilities. Remedial and SpecialEducation, 24(4), 235–245.

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Chard, D., Clarke, B., Baker, S., Otterstedt, J., Braun, D., Katz, R. (2005). Usingmeasures of number sense to screen for difficulties in mathematics:Preliminary findings. Assessment for Effective Instruction, 30(2), 3–14.

Christ, T. J., & Vining, O. (2006). Curriculum-based measurement procedures todevelop multiple-skill mathematics computation probes: Evaluation of randomand stratified stimulus-set arrangements. School Psychology Review, 35,387–400.

Clarke, B, Baker, S., Smolkowski, K., & Chard, D. J. (2008). An analysis of earlynumeracy curriculum-based measurement: Examining the role of growth instudent outcomes. Remedial and Special Education, 29, 46–57.

Clarke, B., & Shinn, M. R. (2004). A preliminary investigation into the identificationand development of early mathematics curriculum-based measurement. SchoolPsychology Review, 33(2), 234–248.

Elliott, S.N., & Fuchs, L.S. (1997). The utility of curriculum-based measurement andperformance assessment as alternatives to traditional intelligence andachievement tests. School Psychology Review, 26(2), 224–233.

Epstein, M. H., Polloway, E. A., & Patton, J. R. (1989). Academic achievementprobes: Reliability of measures for students with mild mental retardation.Special Services in the Schools, 5(1/2), 23–31.

Evans-Hampton, T. N., Skinner, C. H., Henington, C., Sims, S., & McDaniel, C.(2002). An investigation of situational bias: Conspicuous and covert timingduring curriculum-based measurement of mathematics across African Americanand Caucasian students. School Psychology Review, 31(4), 529–539.

Foegen, A. (2000). Technical adequacy of general outcome measures for middleschool mathematics. Diagnostique, 25(3), 175–203.

Foegen, A. (in press). Progress monitoring in middle school mathematics: Optionsand issues. Remedial and Special Education.

Foegen, A. (2008). Algebra progress monitoring and interventions for students withlearning disabilities. Learning Disability Quarterly, 31, 65–78.

Foegen, A., & Deno, S. L. (2001). Identifying growth indicators for low-achievingstudents in middle school mathematics. Journal of Special Education, 35, 4–16.

Foegen, A., Jiban, C., & Deno, S. (2007). Progress monitoring measures inmathematics: A review of the literature. The Journal of Special Education, 41,121–139.

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Foegen, A., Olson, J. R., & Impecoven-Lind, L. (in press). Developing progressmonitoring measures for secondary mathematics: An illustration in algebra.Assessment for Effective Intervention 33(4).

Fuchs, D., Fuchs, L.S., & Fernstrom, P. (1992). Case-by-case reintegration ofstudents with learning disabilities. Elementary School Journal, 92(3), 261–281.

Fuchs, D., Fuchs, L. S., & Fernstrom, P. (1993). A conservative approach to specialeducation reform: Mainstreaming through transenvironmental programming andcurriculum-based measurement. American Educational Research Journal, 30(1),149–177.

Fuchs, L. S. (2004). The past, present, and future of curriculum-basedmeasurement research. School Psychology Review, 33(2), 188–192.

Fuchs, L.S., & Fuchs, D. (1993). Formative evaluation of academic progress: Howmuch growth can we expect. School Psychology Review, 22(1), 27–49.

Fuchs, L.S., & Fuchs, D. (2002). Curriculum-based measurement: Describingcompetence, enhancing outcomes, evaluating treatment nonresponders.Peabody Journal of Education, 77(2), 64–84.

Fuchs, L. S., & Fuchs, D. (2002). Mathematical problem-solving profiles of studentswith mathematics disability with and without comorbid reading disabilities.Journal of Learning Disabilities, 35(6), 563–573.

Fuchs, L. S., Fuchs, D., Bentz, J., Phillips, N. B., & Hamlett, C. L. (1994). The natureof student interactions during peer tutoring with and without training andexperience. American Educational Research Journal, 31, 75–103.

Fuchs, L. S., Fuchs, D., Eaton, S. B., & Karns, K. M. (2000). Supplementing teacherjudgments of mathematics test accommodations with objective data sources.School Psychology Review, 29(1), 65–85.

Fuchs, L. S., Fuchs, D., & Hamlett, C. L. (1989). Computers and curriculum-basedmeasurement: Effects of teacher feedback systems. School PsychologyReview, 18(1), 112–125.

Fuchs, L. S., Fuchs, D., & Hamlett, C. L. (1989). Effects of alternative goalstructures within curriculum-based measurement. Exceptional Children, 55,429–438.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Allinder, R. M. (1989). The reliability andvalidity of skills analysis within curriculum-based measurement. Diagnostique,14(4), 203–221.

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Fuchs, L. S., Fuchs, D., Hamlett, C. L., Phillips, N. B., & Bentz, J. (1994). Classwidecurriculum-based measurement: Helping general educators meet the challengeof student diversity. Exceptional Children, 60, 518–537.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Stecker, P. M. (1990). The role of skillsanalysis in curriculum-based measurement in math. School Psychology Review,19(1), 6–22.

Fuchs, L. S., Fuchs, D., Hamlett, C. L. & Stecker, P. M. (1991). Effects ofcurriculum-based measurement and consultation on teacher planning andstudent achievement in mathematics operations. American EducationalResearch Journal, 28, 617–641.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., Thompson, A., Roberts, P. H., Kubek, P., &Stecker, P. M. (1994). Technical features of a mathematics concepts andapplications curriculum-based measurement system. Diagnostique, 19(4),23–49.

Fuchs, L. S., Fuchs, D., Hamlett, C. L., Walz, L., & Germann, G. (1993). Formativeevaluation of academic progress: How much growth can we expect? SchoolPsychology Review, 22, 27–48.

Fuchs, L. S., Fuchs, D., Phillips, N. B., Hamlett, C. L., & Karns, K. (1995).Acquisition and transfer effects of classwide peer-assisted learning strategies inmathematics for students with varying learning histories. School PsychologyReview, 24(4), 604–620.

Fuchs, L. S., Fuchs, D., Prentice, K., Burch, M., Hamlett, C. L., Owen, R., Hosp, M.,& Jancek, D. (2003). Explicitly teaching for transfer: Effects on third-gradestudents’ mathematical problem solving. Journal of Educational Psychology,95(2), 293–305.

Fuchs, L. S., Hamlett, C. L., & Fuchs, D. (1998). Monitoring basic skills progress:Basic math computation (2nd ed.). Austin, TX: PRO-ED.

Fuchs, L. S., Hamlett, C. L., & Fuchs, D. (1999). Monitoring basic skills progress:Basic math concepts and applications. Austin, TX: PRO-ED.

Helwig, R., Anderson, L., & Tindal, G. (2002). Using a concept-grounded,curriculum-based measure in mathematics to predict statewide test scores formiddle school students with LD. Journal of Special Education, 36, 102–112.

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Helwig, R., & Tindal, G. (2002). Using general outcome measures in mathematics tomeasure adequate yearly progress as mandated by Title I. Assessment forEffective Intervention, 28(1), 9–18.

Hintze, J.M., Christ, T.J., & Keller, L.A. (2002). The generalizability of CBM survey-level mathematics assessments: Just how many samples do we need? SchoolPsychology Review, 31, 514–528.

Jiban, C. L., & Deno, S. L. (2007). Using math and reading curriculum-basedmeasurements to predict state mathematics test performance: Are simple one-minute measures technically adequate? Assessment for Effective Intervention,32, 78–89.

Jitendra, A. K., Sczesniak, E., & Deatline-Buchman, A. (2005). Validation ofcurriculum-based mathematical word problem solving tasks as indictors ofmathematics proficiency for third graders. School Psychology Review, 34,358–371.

Leh, J. M., Jitendra, A. K., Caskie, G. I. L., & Griffin, C. C. (2007). An evaluation ofcurriculum-based measurement of mathematics word problem-solvingmeasures for monitoring third-grade students’ mathematics competence.Assessment for Effective Intervention, 32, 90–99.

Lembke, E. S., Foegen, A., Whittaker, T. A., & Hampton, D. (in press). Establishingtechnically adequate measures of progress in early numeracy. Assessment forEffective Intervention, 33(4).

Mathes, P. G., Fuchs, D., Roberts, P. H., & Fuchs, L. S. (1998). Preparing studentswith special needs for reintegration: Curriculum-based measurement’s impacton transenvironmental programming. Journal of Learning Disabilities, 31(6),615–624.

Nolet, V., & McLaughlin, M. (1997). Using CBM to explore a consequential basis forthe validity of a state-wide performance assessment. Diagnostique, 22(3),146–163.

Phillips, N. B., Fuchs, L. S., & Fuchs, D. (1994). Effects of classwide curriculum-based measurement and peer tutoring: A collaborative researcher-practitionerinterview study. Journal of Learning Disabilities, 27(7), 420–432.

Phillips, N. B., Hamlett, C. L., Fuchs, L. S., & Fuchs, D. (1993). Combiningclasswide curriculum-based measurement and peer tutoring to help generaleducators provide adaptive education. Learning Disabilities Research andPractice, 8 (3), 148–156.

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Shinn, M., & Marston, D. (1985). Differentiating mildly handicapped, low-achieving,and regular education students: A curriculum-based approach. Remedial andSpecial Education, 6 (2), 31–38.

Spicuzza, R., Ysseldyke, J., Lemkuil, A., Kosciolek, S., Boys, C., & Telluchsingh, E.(2001). Effects of curriculum-based monitoring on classroom instruction andmath achievement. Journal of School Psychology, 39, 521–542.

Stecker, P. M., & Fuchs, L. S. (2000). Effecting superior achievement usingcurriculum-based measurement: The importance of individual progressmonitoring. Learning Disabilities Research and Practice, 15(3), 128–134.

Stecker, P. M., Fuchs, L. S., & Fuchs, D. (2005). Using curriculum-basedmeasurement to improve student achievement: Review of research.Psychology in the Schools, 42, 795–819.

Stoner, G., Carey, S. P., Ikeda, M. J., & Shinn, M. R. (1994). The utility ofcurriculum-based measurement for evaluating the effects of methylphenidateon academic-performance. Journal of Applied Behavior Analysis, 27(1),101–113.

Thurber, R.S., Shinn, M.R., & Smolkowski, K. (2002). What is measured inmathematics tests? Construct validity of curriculum-based mathematicsmeasures. School Psychology Review, 31, 498–513.

Tindal, G., Germann, G., & Deno, S. L. (1983). Descriptive research on the PineCounty norms: A compilation of findings (Research Report No. 132).Minneapolis: University of Minnesota Institute for Research on LearningDisabilities.

Tindal, G., Marston, D., & Deno, S. L. (1983). The reliability of direct and repeatedmeasurement (Research Report No. 109). Minneapolis: University of MinnesotaInstitute for Research on Learning Disabilities.

VanDerHeyden, A. M., Broussard, C., Fabre, M., Stanley, J., LeGendre, J., &Creppell, R. (2004). Development and validation of curriculum-based measuresof math performance for preschool children. Journal of Early Intervention, 27(1),27–41.

VanDerHeyden, A. M., Witt, J. C., & Naquin, G. (2003). Development and validationof a process for screening referrals to special education. School PsychologyReview, 32(2), 204–227.

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VanDerHeyden, A. M., Witt, J. C., Naquin, G., & Noell, G. (2001). The reliability andvalidity of curriculum-based measurement readiness probes for kindergartenstudents. School Psychology Review, 30(3), 363–382.

Whinnery, K. W., & Fuchs, L. S. (1993). Effects of goal and test-taking strategies onthe computation performance of students with learning disabilities. LearningDisabilities Research and Practice, 8 (4), 204–214.

Whinnery, K.W., & Stecker, P. M. (1992). Individual progress monitoring to enhanceinstructional programs in mathematics. Preventing School Failure, 36(2), 26–29.

Ysseldyke, J., Spicuzza, R., Kosciolek, S., Teelucksingh, E., Boys, C., & Lemkuil, A.(2003). Using a curriculum-based instructional management system to enhancemath achievement in urban schools. Journal of Education for Students Placed atRisk, 8, 247–265.

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ARTICLES ON THE EARLY HISTORY OF PROGRESS

MONITORING READING AND MORE RECENT

APPLICATIONS

Deno, S. L. (1985). Curriculum-based measurement: The emerging alternative.Exceptional Children, 52, 219–232.

Deno, S. L. (1992). The nature and development of curriculum-based measurement.Preventing School Failure, 36 (2), 5–10.

Deno, S. L. (2003). Developments in curriculum-based measurement. The Journalof Special Education, 37, 184–192.

AN INTRODUCTION TO PROGRESS MONITORING IN MATHEMATICS

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